Is it possible to set up a process( which notifies me via some sort of icon on
taskbar try like email alert does) which monitors a particular directory on
my computer and if a new file is added to that directory, triggers the alert?
If so, if anyone can point me in the direction it would be appreciated.

You can use inotify or fsniper with a script and notify-send
Take a look at incron. I would use it and make it call a script that shows the popup.

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